Non-Abelian statistics with mixed-boundary punctures on the toric code
arXiv:2103.08381 · doi:10.1103/PhysRevA.105.042417
Abstract
The toric code is a simple and exactly solvable example of topological order realising Abelian anyons. However, it was shown to support non-local lattice defects, namely twists, which exhibit non-Abelian anyonic behaviour [1]. Motivated by this result, we investigated the potential of having non-Abelian statistics from puncture defects on the toric code. We demonstrate that an encoding with mixed-boundary punctures reproduces Ising fusion, and a logical Pauli- upon their braiding. Our construction paves the way for local lattice defects to exhibit non-Abelian properties that can be employed for quantum information tasks.
References in corpus (10)
- Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
- Surface codes: Towards practical large-scale quantum computation
- Topological fault-tolerance in cluster state quantum computation
- Topological Order with a Twist: Ising Anyons from an Abelian Model
- Genons, twist defects, and projective non-Abelian braiding statistics
- Projective non-Abelian Statistics of Dislocation Defects in a Z_N Rotor Model
- A Description of Kitaev's Honeycomb Model with Toric-Code Stabilizers
- Simple scheme for encoding and decoding a qubit in unknown state for various topological codes
- Non-abelian statistics from an abelian model
- Equivalence between vortices, twists and chiral gauge fields in Kitaev's honeycomb lattice model